## Mathematical Morphology in Image ProcessingPresents the statistical analysis of morphological filters and their automatic optical design, the development of morphological features for image signatures, and the design of efficient morphological algorithms. Extends the morphological paradigm to include other branches of science and mathematics.;This book is designed to be of interest to optical, electrical and electronics, and electro-optic engineers, including image processing, signal processing, machine vision, and computer vision engineers, applied mathematicians, image analysts and scientists and graduate-level students in image processing and mathematical morphology courses. |

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### Contents

Training Structuring Elements in Morphological Networks | 1 |

Efficient Design Strategies for the Optimal Binary Digital Morphological Filter Probabilities Constraints and StructuringElement Libraries | 43 |

Statistical Properties of Discrete Morphological Filters | 93 |

Morphological Analysis of Pavement Surface Condition | 121 |

On Two Inverse Problems in Mathematical Morphology | 151 |

Graph Morphology in Image Analysis | 171 |

Mathematical Morphology with Noncommutative Symmetry Groups | 205 |

Morphological Algorithms | 255 |

Discrete HalfPlane Morphology for Restricted Domains | 289 |

On a Distance Function Approach for GrayLevel Mathematical Morphology | 323 |

Invariant Characterizations and Pseudocharacterizations of Finite Multidimensional Sets Based on Mathematical Morphology | 351 |

The Morphological Approach to Segmentation The Watershed Transformation | 433 |

Anamorphoses and Function Lattices Multivalued Morphology | 483 |

525 | |

### Common terms and phrases

algorithms anamorphoses applied B-code basic irregular images bijective binary image Boolean function catchment basins characterization clos-opening closing complete lattice computation Consider convex convolution corresponding defined Definition denoted dilation dilations and erosions discrete discrete signal distance function distress distribution function edges equivalent erosion Euclidean Euclidean distance example Gabriel graph geodesic given gradient graph gray-level gray-tone half-plane Hebbian learning Hence homogeneous space identity mapping IEEE image analysis image F Image Processing input invariant lattice points Lemma markers mathematical morphology Matheron matrix minima Minkowski addition morphological filters morphological operations noise obtained opening distributions optimal ordered queue output pixels Proof properties Proposition rank-order operator reconstruction representation respectively restricted domain result s-graph scanning Section segmentation Serra shape shown in Figure signal skeleton SKIZ stack filter structuring element subset texture scale Theorem threshold tion totally ordered translation values vector vertex vertices watershed algorithm